Vibbation absobbeb



C. R. SC)DERBERG` June.6,'1933 VIBRATION ABSORBER R,v 18,861

Original Filed April 2', 1924 3 Sheets-sheet 1 lwnNE s; l IMI/ENTQR Cczr/ R Sade/fbg@ www ATTORNEY C. R. SODERBERG 5 Sheets-Shea?, 2

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June 6, 1933. VIBRATION ABsoRBER original Filed Apil 2, 1924 INVNTR (ar/ Sade/*bey l, f ATTORNEY 1 v c. RSODRBERG June 6 1933 VIBRATION ABsoRBER y Re 18,861

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u I BY S NTM U a/m/ ATTORN EY Reissued June 6v, 1933 o UNITED *STATES "Re 18,861l f PATENT OFFICE CARL R. SODERBEB'G, OF SWARTHMURE, PENNSYLVANIA, ASSIGNOR TO WESTING- HOUSE ELECTRIC & MANUFACTUING COMPANY, AfCORPORATION F PENNSYL- VAN'IA d 'VIBRATION ABSORBER original mi. isaesaiaatea August 1e, 1927, serii No. 703,830, iiiea Aprii 2, 1924. Application ro reissue led September 30,k

My `inventionrelates to vibration absorby ers and it has particular relation to vibration tion that is different from the frequency of foundation.

absorbers for suppressing undesirable effects produced by periodically varying forces.,

The present invention-has been developed in connection with dynamoelectric machines wherein a periodically )pulsating torque transmitted from the stator to the rotor produces pulsating reactions between the stator and foundation, which, in turn, result in foundation failures or in other highly undesirable effects.

It was early recognized that the problem of reducing the effect of periodically varying forces acting upon a foundation or the like is radically different from the` problem of reducing the effect of irregularly occurring impulses. Thus, it has been realized that a mechanical system which is exposed to the action of periodically varying forces should have a natural frequency of vibrathe impressed forces, in order to avoid disastrous resonance effects multiplying the magnitude of the forces transmitted to the In analyzing the problem of vibration absorption as met in dynamo-electric machines of the above-mentioned character, I have found that the principles which governed the prior designs of vibration absorbers while avoiding the actual dangers caused by resonance effects, did not actuallyslead'to constructions which diminish the magnitude of the forces transmitted-to the`foundation, but merely prevented an excessive increase of the same. I have found that by preserving a` certain definite relation between/the natural period of vibration of the system .exposed to: the periodically varying'forces '.rand the period of oscillation of said forces,

vibration. absorbers may be constructed which not only remove the dangers of resonance between the two' frequencies but actually diminish the magnitude of the variations of the forces transmitted to the foundation.

One object of my invention is, therefore, to provide vibration absorbers that will rel duce the magnitude of they variations of the 1932. Serial No. 635,640.

transmitted force as compared to'the variations of the disturbing force4 acting thereon.

Another object is to provide vibration ab-r sorbers constituting, in connection with the vlbr'ating body, a mechanical system having a natural frequency that is equal to, or less 1 than, #i of the frequency of the impressed tric machine, are torsional and tend to rotate the same, the reactive forces transmitted to the foundation bythe stator must also be torsional, It is important that vibration absorbers designed for such machines shall positively prevent the introduction of forces tendingw to displace the stator from its central position. As fas ar I am aware, des1gners of vibration absorbers utilized `heretofore in machines of the above-'designated character did not realize the effect of the introduction of translational forces by impropeidesign of the vibration absorbers.

Accordingly, While attempting to reduce the effect of the undesirable variation of the torque, the vibrating body has been subjected to periodically Varying translatory forces tending to displace the stator from its central position and thus impairing, to a large degree, the beneficial effects of the vibration absorber.

y Accordingly, another object of my invention is to so design vibration absorbers for bodies exposed to periodically varying torsional forces as to resiliently loppose the action of said forces, withoutimparting to said body forces tending to change the path of the motion of the same.

Other objects of my invention relate to the details of construction of vibration absorbers whereby the available space is best utilized and a maximum absorbing effect is secured with a minimum of material.

With the foregoing and other objects in view, my invention will best be understood by reference to the accompanying drawings wherein;

Flgure l 1s a view in front elevation illusabsorber,

Fig. 3 is an elevational View ofv one #of the vibration absorbers shown in Fig. l, and

illustrating the same more in detail,

Fig. 4 is a sectional view along the line IV-IV of Fig. 3,

Figs. 5 to 7 are views similar to Fig. 3, of modifications of my invention,

Fig. 8 is a view similar to Fig. 2, of a further modification,

Figs. 9 to 17 are diagrams utilized to eX- plain various features of my invention and referred to more fully hereinafter, and

Fig. 1'8 is a sectional view along the line XVIIIXVIII of Fig. 7.` I

Referring to Figs. 1 and 2, a motor-generator set is shown comprising a polyphase motor 1 and Va single-phase generator 2, the rotors of the two machines being mounted on a common shaft 3 supported by pedestal bearings 4 that are rigidly secured to. a bed plate 5 constituting a part of the foundation. The stator members 6 and 7 of the polyphase motor 1 and the single-phase generator 2, respectively, are connected to the bed plate 5 and are held in a position concentric withthe rotors. Since the power delivered to the polyphase motor is substantially continuous, and that delivered by the single-phase generator is periodically varying, corresponding to the alternations of the single-phase power delivered by the same, the stator 7 of the single-phase machine will transmit to ,the bed plate 5, torsional reactive forces that vary periodically in the same manner as the power delivered by the singlephase machine. 4

' In order to eliminatethe dangerous effects of the vibratory forces acting upon the foundation, the stator member of the singlephase machine is provided with resilient means or vibration absorbers for making the torque-transmitting connection between the bed plate and the stator member. In the illustrated form of my invention,'which is also the preferred form, the stator member 7 ofthe single-phase generator provided,A at the diametrically opposed portions 10 and 11, with lateral,ihorizontally disposedextensions 12 and 13 which are secured to the foundations by means of vibration absorbers 14.

As shown more in detail in Figs. 3 and 4, each vibration absorber comprises a pedestal member 15 secured to the bed plate 5 and extending upwardly for engagement with the horizontal stator extensions 12 and 13.

In the preferred construction shown in the drawings thestator is made of upper and lower` halves 16 and 17, respectively, the two halves being secured to each other by 'means of flanges 18 and 19 meeting in a substantially horizontal plane and'secured to each other by means of a plurality-of bolts 20. The flanges 18 and 19 of the stator constitute the lateral stator extensions 12 and 13 mentioned hereinbefore.

The torque-transmitting connection between each of the pedestals 15, which are secured to the bed plate, and the corresponding lateral extension'12 or 13 of the stator is effected by means of a lower spring aggregate 22 and Van upper spring aggregate 23.

The lower spring aggregate 22 comprises a' pair of liat plates or beam springs 24 of steel,

supported attheir ends upon the elevated end portion 25 of a steel plate 26 resting upon a horizontal extension Two pressure blocks 28, spaced from each other and from the supporting points of the beam springs, are secured in grooves extending radially in the lower side of the lateral stator extension 12 or 13 and transmit the reaction of the stator to the lower springs 24.

The upper spring aggregate 23 comprises two beam springs 31 of rectangular cross-sec-M tion similar to the lower springs 24 and supported at their ends upon a pair of radially disposed pressure blocks 32 extending somewhat above the upper level of the lateral eX- tension 12 or 13. A yoke 33 is disposed above the upper springs 23 and engages the same at mid-points 34 by means of a pressure block 35 of tempered steel extending downwardly from the lower surface ofthe` yoke.v The yoke 33 is spaced in fixed relation to the pedestal extension 27 by means of a plurality of tensioning bolts 36 clamping the whole spring assemblytogether.

The construction illustrated in Figs. 1 to 27 of the pedestal 15.V

4 is intended for large machine units as, in

general, the difficulties arising from the periodically varying torque is of primary iinportance mainly in connection with large machines. In any vibration-absorber-construction utilized in connection with a dynaino-electric machine,it is imperative to maintainthe concentric position of the stator with respect to the rotor, notwithstanding the arrangement of the vibration absorber.

and the operation of the same. It is accordingly usual practice to provide a rigid connection between the stator and the rotor shaft, asby means of end brackets secured to the stator and having trunnions surrounding the shaft. Such constructions are, in general, very b'ulky on account of the large dii mensions of the co-operating machine members, and are particularly objectionable in large machines because of the intolerably large increase in the weight, as well as in the space, required by such machines. According to my present invention I depend entirely upon the vibration absorbers 14 for maintaining the stator in a central position whileat the same time reducing the vibrations.

In the construction shown in Figs. 1 to 4, the weight of the stator, acting upon the loweri springs 24 through the pressure sioning bolts 36, toward the lateral extension 27 of the pedestal 15 and-compresses the upperspring until the stator is brought into its final position with respect to the rotor. The p rovisionl of the upper spring aggregate 23 and of the yoke 33 prevents the` stator from being'thrownvupwardly under the action of excessive jolts acting upon the stator, and at the samey time, the upper spring aggregate is so arranged as to limit the movement of the lower springs to a range wherein thesame are continually compressed in the downward lldiretion. The significance of the last-mentioned feature will be pointed out later. The angular-Inovement of the stator against the action of the l springs tending to maintain the same in a neutral horizontal position is limited by means of keys 37 of tempered steel limiting the downward movement of the stator extensions 12 or 13 and akey 38 of tempered steel limiting the'upward movement ot the stator extension.- A

In the preferred construction 'illustrated in Figs. 3 and V4, movements of the stator in an axial direction are prevented by flanges 41 extending from the, sides of the flanges 18 and 19, and having vertical faces 42 bearing against co-operating surfaces 43 of the pedestalsJ 15 and spring assemblies 22fand 23, while radial movement of the stator in horizontal direction is prevented by substantially circularly shaped bearing portions 44 of the stator 3o-operating with cooperating bearing faces of the pedestals 15. If desired, light retaining or covering plates 45 may be screwed onto the members 33 and 27, as shown in Fig. 4, to retain theiouter spring members 31 and 24.

In the design of the vibration absorbers employed .1 the machine shown in Figs. 1 to 4, I have employed certain principles which will best begfexplained by considermg the problem of vibration absorption in asomewhat simplified and more generalized way.

General principles v `Referring to Fig. 10, let us consider (a mechanical system comprising a body 51 of mass M supported or cushioned upon a foundation 52 by two spring members .53, and subjected to a variable orce F acting cen-b trally upon the body in vertical directlon.

It is the function of the vibration absorber to provide such connection between4 the foundation 52 and thebody 51 which is acted upon by the variable force, as to make the force transmitted to the foundation as small as possible, and the effectiveness of the vibration absorber will be measured by the ratio of the force acting upon the foundation to the force acting upon the supported body. I term that ratio the transmitting eiect e of the ,vibration absorber and (1 6) the cushioning effect of the vibration absorber.

The impressed force s periodical Let it be assumed now' that theforce acting upon the supported body 51 is a periodic harmonic force given by the equation F =F,.`sin wt in pounds,

ythree groups of reactional forces: the inertia reaction Rgthe elastic reaction of the springu support RB and\damping forces Rd. The expression for the relation of the forces may be derived from the equation for the motion of the mass M of the body 51.

The motion of a point of the mass under the iniiuence of the periodic. force F is expressed hy the equation wm sin (wr-s) (2) where a: isthe deflection of a point from the v positibn which it assumes when the reaction of the spring member is equal to the steady load, wm is'the maximum amplitude of the periodic defiection and I is an angle expressing the difference in phase between the oscillation of vthe impressed forceand'- the oscillatory movement of the mass M. 1 The reactional forces will then be as folows:

RFM-Mwa.. sin (wt-c+ 180) (s) 'dzx dm (6) I F M kx 'c and 'is represented vectorially in Fig. 4v11 in the,manner usual in treating alternating- SOy The reaction on` the foundation is the vectorial sum of the spring reaction and the` damping reaction. A part of thelatter Will be represented by air resistance Which will vsion not react on the foundation. N eglecting this effect we have as thereaction on the foundation y i fa=wmm (9) Neglecting the damping, vve haveA The physical significance of the derived expressions will appear more clearly by 1ntroducing an expression for the resonance speed of the system, or the angular velocity corresponding tothe natural period of the mechanism, and an expresfor the damping coefficient of the motion.

The resonance speed w, is obtained by equating the second term in thedenominator of Equation (8') to zero which corresponds to the condition of maximum amplitude of the oscillation.

4 Substituting expressions (11) and (12) in (10) and (10a) We have reet-er1 The curves in Fig. 18 represent1 the' transmitting eject e as a function of the ratio g. of the operating speed to the resonance undamped oscillation; another-curve cor-- responding to the condition 8:04, Where the damping reduces the amplitude of the oscillation torone one-hundredth of vits original .value in 3.5 cycles, and a still other curve corresponding to an aperiodic system with 8=2. Y

As far as I am aware, designers of vibration absorbing devices known in the prior art believed that all that was necessary to make a good vib-ration absorber was to make the resonance ,velocity of the system different from the operating velocity. The design was a hit-or-miss proposition. Sometimes unexpectedly good results Were obtained, and sometimes equally unacoountably poor results would be obtainedn However, from the curves in- Fig. 13, it

may be seen that merely making the reso-v nance frequently 'different from the operating frequency is not the only criterion, and that the transmitting effect is 4above one for all y valuesiof wg smaller than approximately c v i 1/= 1.41, y, i. e., the force transmitted tothe foundation 1 is larger than thedisturbing periodical force F and such Vibration absorberis in fact detrimental, although its resonance velocity is different from the operating velocity. Thus, i

no cushioning.y is obtained if the resonance speed is above about 70% of the operating speed. he prior-art' requirement merely tried to avoid making the natural period of the systemof the order oftheperiodicity `of the disturbance but did not otherwise discriminate which frequency. shall be Vlarger and Which smaller. In orderto obtain a considerable cushioning it is necessary to place the resonance speed at one-third to onefourth of the operating speed. For example, with a louT damping, the transmitting effect is only 0.1 when .the operating speed is 3.32 times the resonance speed.

The eil'ect of damping upon the performance ofthe vibration absorber requires special consideration. In the range wherein the vibration absorber acts detrimentally, large damping reduces the transmitting effeet and thus acts beneficially. It is advisable, therefore, to introduce damping Whenever a system operates Within a range where the operating velocity is less than 1.41 of the resonant velocity. On the contrary, when operating at higher velocities, a reduction in the damping produces a reduction in the transmitting effect and is then beneficial.

The Equation (8), expressing the motion of the suspended body, may be Written` in will be diminished in proportion to the transi initting effect of the vibration absorber.

the cushioned mass given in Equation (14)` is represented asa function of theratloof the impressed velocity to the resonance velocity in Fig-A4, for di'erent values of the damping factor. Thev motion of the cushv e w loned mass grows from a value k for =0 J w to a maxlmum value at resonance, g 1, and

diminishes asymptotically to zero.

By comparing Figs. 13 and 14, it appears that the motion ofthe cushioned mass is re- Atic properties lduced in proportion to the transmitting effect of the vibration absorber. In contradiction to the usual belief`,'the motion of the" cushioned mass is reduced as the cushioning effect (l-e is improved, or as'the periodical force transmitted to the foundation is rel duced.

In the foregoing analysis of the principles of vibration absorbers, I have assumed .that the foundation is rigid, (b) that 'the spring has a 'straightdine characteristic, or that 7c is constant, and (c) that ideal velocity damping is obtained, i. e., that the damping is directly proportional to the velocity of motion.

The assumption concerning the foundation is purely theoretical.v If such were the case, it would lbe best to make the connection between the supported mass and the foundation rigid permitting the entire magnitude of the 'disturbing force to be transmitted to the foundation; no vibration absorber would be needed.' It is through the imperfect nature of the support that the real problem is created.

n Since no'foundation is perfectly' rigid, the leffects ofvariable foundation maybe entlrely vbeyond control.

forces acting upon the The very necesslty for a vibration absorber indicates that'the foundation possesses elasi of such nature that impulses of the operating frequency produce undesirable results'. Usually, the undesirable results manifest themselves in adjoining structures. It is evident, however, thatas long as the flexibility of the vibration'absorber is great in comparison with that of the foundation itself, the former, 'if properly con-l structed, willV accomplish a reduction of the impressed impulses.` Thiais all thatcanbe expected; the foundation and the ad]oin1ng structures will remain receptive tothe same frequencies as before, but the disturbances l Fm 1 t wz fai-; 52002' v wz fr?) wil-.) l

'The amplitude of the lvibratory motion of the rigidity or .'Naturally, a more flmdamental measure would be to change either the operating frec luency or the elastic properties ofthe ad- ]oining structures. The proper application of vibration absorbers should be restricted to cases Where such measures are impossible.

The assumption ofthe constant scale of the vibration absorber is'alsov of atheoretical nature. As .a matter of fact, it is usually desirable to arrange vibration absorbers with a risingv scale in order to limit the maximum lstress for extreme load conditions.

This does not affect our results, however. `It

is merely necessary to consider the range of sprlng scale that ocurs .within the range of the load'. The'cushioning eectwill be a function of the load; naturally the arrangement should be`such that at the maximum load the cushioning effect of thevibral i tion absorber is a maximum. 'In most practical cases, the vibratory deiections of the vibration absorber, for a specific load, are so small that the assumption of a4 constant spring scale is correct.V

The assumptlons concerning the' damping 'are approximately correctfor vibration absorbers of organic materials having high internal friction. In other cases, the damping will be produced byrubbing friction which does not conform to the velocity/law.

As shown hereinbefore, vthe damping is detrimental foi-ordinary cases of vibration absorption, so uthat nothingl willbe gained Aby the introduction of friction, of irregular variations of the disturbances. Furthermore, the effects of a 'moderate amount of damping are very small.-` The real objectionto internal friction in the material forvvibration absorbers is-the deterioration 'resulting' fromu such damping. Mechanical',friction is even more detrimental than-the friction damping which has `been vconsidered in our analysis. It is desirable,

therefore, to arrange the design in such a except in cases i mannerthat mechanical friction is avoided.I

The foregoing analysis is valid for 'avariety of mechanical arrangements. It is only necessary that the ysystem shall have one degree of freedom and, consequently, one resonance speed. For example,` it will apply lequally well ,to a flexible couplingbetween two rotating shafts as to a iiex'ible support for the stator of an electric machine. The expressions for the resonance'speed andv for the damping must, of course, be adjusted to suit the specific system. Y

In our present case of a rotative system, the spring scale' represents a torsional spring scale in inch-pounds per radian and the mass M must be replaced by the moment of inertia. r o

The-required 'volw/me of spring material vention, it 'is possible to fully design the vibration absorber with any desired degree of effectiveness and with the best utilization of material and space.

Vibration absorbers may be made either of steel springs or of different kinds of organic materials, such as leather, rubber, Wood, cork and various compounds. A great deal of experimenting. has been done with vibration absorbers of the latter kind.

' The results are most varied, presumably because all factors have not been properly taken. into account in the design. Steel springs must-be used in all cases where a heavy load has to be carried.

The` most objectionable properties of the organic materials, vibration absorbers, are the variable elastic properties, and the deterioration caused by aging and internal frictionf The internal friction is not always undesirable in itself, provided that it is obtained without destruction of the absorbers.

Most of the organic materials have the property of a variable modulus of elasticity for varying loads. In order to apply such vibration 'absorbers intelligently lit is necessary to have a thorough knowledge of their elastic properties.n It is usually necessary to studythese properties in test pieces of full size because the properties vary for/pads of dili'erent dimensions.'

As a general rule, it may be stated that the results are always uncertain when organic f materials are used.

I prefer to employ flexible members gf steel, which may be arranged to have all the desirable properties of organic materials and none of their disadvantages.

In applying the foregoing principles to the design of a lvibration absorber, such as that shown in Figs. 3 and 4, it is best to select the degree of flexibility which gives a tolerable valueof transmitting effect. It is desirable to'make the transmitting effect as low ow enough to place the 'resonance speed at in their application to as possible, but as soon as the flexibility is 1 V l one-third to one-fourth of the operating` speed, additional flexibility produces very slight gain in the cushioning effect, as shown in Fig. 12. The fact just `mentioned is of considerable importance, because a seemingly impossible application may frequently be Y reduced to a feasible casebya slight reduct1on in the requirements of cushioning.

If the vibration absorber has to carry a certainmaximum load P, under which 'it defiects a certain amount the potential l energy U, which it'absorbs for this deflection is,- f U51; (15) If the spring scale of the vibration absorber is lo We have P=cx or x =I3 (16) i P2 The units of the quantities in these expressions should, of course, specific arrangement under consideration. If P is a moment in inch-pounds, will be a torsionalI spring scale in inch-pounds per radian and a: will represent an angle in radians. If P is a force in pounds, 7c will be a linear spring scale in pounds per inch and a: will be a length in inches. stances U will be expressed in inch-pounds.

With a given operating frequency, the

transmitting effect is smaller the smaller the resonance velocity smaller the spring-scale k. i This means,

when considered in I connection with expression (17), that the effectiveness of a vibra correspond to the In both intion absorber depends on its lability to'absorb potential energy.

If a certain element of volume dv of the spring-material is under a certain stress p and its modulus of elasticity is E, the potential energy absorbed by virtue of this stress will be o vThe total potential energy of the spring member is, therefore,-

The integration should be extended ,to allV 2a stress pm and the volume of spring lmate-- rial 'v P2 z l v str1-)ma (21.)

The coellicient 'a represents the efficiency of the loading a 1 1d 'expresses the degree to which the different elements of a spring are brought into stress, or the extent to which )the stress in all the different elements of a spring .approaches the maximum stress to which the spring is subjected. Its maximum value is unity, which occurs for a member in straight tension, lall th/eelementsof such 'member being under the same stress. AIn case of steel, the modulus of elasticity E has the value X10 when the stress pm represents tension or compression, and a value of 11.5Xl0- when the stress pm ,represents shearing.

By equating Equations (17) and (20) we obtain an expression giving the relation between the load P, the scale k, the'maximum :5 sorber with a transmitting effect e.

Equation is especially. usefl lin the preliminary design of vibration absorbers.-

The possibility of obtaining al sufficient amount of cushioning depends upon whether o or not it is possible to find room for-'the required volume of spring material. I accordingly so arrange the vibration absorber as to make thevolume 'v a minimum'for a i given transmitting effect, by making the co- "J eiicient of loading a a maximum.

In the following table are given the values of the loading coeilicient `for different ari rangements of steel springs'illustrated diagrammatlcally 1n Fig. 15. f

CEggilg of Kind of spring Efiiciency of loading Straight tension Rod of uniform crossa=1.0. or compression. section (64).

Torsion. Round rod of uniform a=.5

cross-section (55). 1 Tension or com- Coiispringoiroundunis 11;:

pression. form cross-section and a 15 n "3'5t0'500 'n turns (56). larger than 4.) Bendingm-; Beam oi rectangular a=.111.

cross-section sup- Cf) ported at ends with concentrated 1oad`in the middle (57).

Bending- Cantilever (58) a=.111. Bending' Beam of length L supa,

ported at ends with a=.222fior i725. i two concentrated a loads at distance a F367 {M 1,1 G5 from auch and (59). L

The loading coellicient depends entirely upon the stress distribution. The potential energy per unit volume depends uponJ the actual -values of the maximum stress and the modulus ofv elasticity as well. tablehas been prepared under the assump- .tion that the modulus of elasticity of steel in shear is 0.385 times the modulus ofv elasticity in tension or compression.

It is evident, ffrom the table, that the required volume ofspringmaterial is largely dependent upon the method' of loading the springs. The configuration of the available space will determine which type of spring In the practical construction of vibration The absorbers, the resilient members, providing the torquetransmitting connection between the body exposed to the disturbing forces and the'foundation, must be so designed as to constitute, in connection with the moving body, a mechanical system having a natural frequency of vibration smaller than of the'frequency of the variations of the dlsturbing forces. The resilient members .which is considerably should have the smallest possible spring scale and should be capable ofstoring a maximum of potential energy. I have' found that flat` spring plates or beam springs are most s'uitable for that purpose, since such springs give a better utilization of the available space than coil springs, notwithstanding the high# wer loading eflicien'cyof the latter. It is the combined effect of the amount of spring volume that may be placed in a given space, the loading eiliciency of the spring and the spring scale that determines the superiority of one construction over another.

Among the several constructions 'that may be employed in connection with beam springs, that' wherein a beam spring is supportgd at two points and loaded at two other points spaced from each other and from said first mentioned two points is most suitable, since it readily permits variations in the spring scale and secures a higher loading efliciency than is possible with .the other spring constructions. The construction employed in the vibrationjabsorber illustrated in and 4 is of that character.

Thereare certain definite requirements introduction of translational unbalancing Figs". y3 f lthat must be fulfilled in order` to avoid the..l

forces .by the operation of the vibration absorber. Such unbalancing forces occur, for instance, in the arrangement shown in Fig..

metrically opposite to the stator axis.

0 ingA points 63 of the stator.

16 where a stator 61 is provided at its base, with a pair of extensions 62 having rolling members 63 which are held in circular grooves 64 for permitting rotational move- 5 ment of the stator around its axis 65. Under the action` of a couple of forces 66, the stator tends to rotatecounter-clockwise. The action of the couple 66 may be counteracted by a couple of forces acting at the support- Such a support, in order to. be effective for reducing the vibrations, would require, however, that the stator shall move out of the circular path to which it is confined. If the movement is 5 restricted to a purely circular path such as in the case illustrated in the drawings, the

forces actingl upon the foundation may be sponding to the conventional supporting points of stators of dynamo-electric machines thus produces laterally acting vibratory forces which are not cushioned by the vibration absorbers and may very often prove disastrous on account of the resonance frequency which the system may have for vibra; tions in lateral directions.

Similar conditions obtain in the arrangement shown in Fig. 17, wherein a stator member 71 is provided with trunnions securing thesame centrally with respect to a shaft 7 2 which is supported on pedestal bear; ings 73 mounted upon the foundation 74. TheY stator is prevented from rotation by means of two spring members 75 acting upon a projection 76 extending downwardly from the stator. A couple of forces 77 tending to rotate the stator is counteracted by a couple VH,of forces' 78 acting through the pedestal bearings 73 and through the spring members Y' 75, respectively. The forces acting 'upon the pedestal bearing are not cushioned by the action of the spring members and the purpose-'of the vibration absorber, therefore, is not well fulfilled.

In the constructionvshown in Figs. 1 to 4, the resilient means preventing therotation of the stator actrperpendicularly to a horizontal plane through the axis of rotation of the stator, at points which are disposed di couple of forces tending to rotate the stator is opposed by resilient springs reacting in the direction of rotation and producing a reactional couple of forces of equal magnitude 66 without introducing translational forces `of rotation of the stator.

Ireaction of. the spring members .produces a tending to remove the stator from its central position.

The arrangement of an upper and a lower spring aggregate on each side of the stator member, as shown schematically in F ig. 9, is intended to provide a -convenient arrangement for determining the central position of the stator when at rest and also to secure the stator from being thrown upwardly under the action of sudden jolts of the machine. In this connection it is important to so design the yupper spring aggregate as to leave the scale of the resilient means acting upon. the stator extension as small as possible. This may be understood by considering the forces acting upon the stator member as shown in F ig. 9. The stator member 81 is provided, at diametrically opposite points, with extensions 82 which are held between lower spring aggregates 83 and upper'spring aggregates 84 that are supported upon the foundation 85. Itis assumed that the reaction of the lower spring aggregates, when at rest, is given by the vectors Sla and Sr.,`V

and the reaction of the upper spring aggregates, when at rest, is given by the vectors T1a and Tra.

Under the action of a couple of forces having a torque Q tending to rotate the stator in the counter-clockwise direction,l the stator is deflectedl from the neutral yhorizontal position by'an angle 0 until the reactions of the spring aggregates 83 and 84 balance the couple. The reaction of the left hand, lower spring member after the stator ,is deflected is given by the vector Sie and that of the righthand,lower spring memV ber by the Vector SN. The diferencebetween the spring reactions underrest and after the stator was deflected by the angle 6 is represnted by the vectors S1 and S, which Yrepresent the reaction of'the lower spring members to the action of the couple Q,

In a similar manner, the difference between the vectors Tm and Tra, representing the reactions of the upper spring members at rest, and the vectors T1., and Tlne representing thel reactions of the upper'spring members after the defiection, gives the resultant reactions T1 and Tr constituting a second couple acting in the same direction as the couple of forces S1 and S, and oppoing the action of the torque Q.

The relations between the forces acting upon the stator may be expressed by the j where t'l is the scale of the upper spring members, la: is the scale of the lower spring members and lis the distance from the poizit of action of the spring members to the center It-is seen that' the perfect couple under all conditions and does not introduce translational forces.

In the case where the stator is supported' upon the lower spring members 83, with the upper spring members omitted, it may occur that the) stator may rotate sufficiently to release one of the spring members, the. righthand spring member 83, for instance, from compression and the further movement of the stator would not be controlled by the reaction constitutingr al perfect couple producing a resultant translational force acting upon the stator tendingto displace the same from the central position. of the functions of the upper spring members to restrict the motion of the stator to a range wherein the lower spring members ll are continuously under compression in the same direction.

It may bexseenl from Equation (24) that the effect of the addition of the upper spring a resultant decrease in the effectiveness -of the vibrationl absorber. A It is, therefore,v important to employ such construction for the u'pper spring member that will make the increase of the resultant spring scaler as small as possible and I accordingly employ a construction wherein a beam spring is support-y ed at its ends and loaded at a in the middle thereof.

As seen from the Tcurves in Figs. 13 and 14, the motion ofthe cushioned mass besingle point comes smaller the" better the vibration ab-1 sorberr operates, that is, the smaller the transmitting effect, (seeEquations 10 and 10g), is. Since the transmitting effect becomes smaller in proportion to the decrease in the spring scale, it is important to make the scale of the springs as small as possible, that is, to use soft springs giving large dej lections. In practical constructions, itis rsufficient to secure the small spring scale for a relatively narrow range of movement around they neutral axis since under normal operation a good vibration absorber should restrict the motion of rthe'stator to such range' only. In order to prevent sudden impacts ,of the stator up`on the supporting members of the foundation when occasionally rotated,` beyond the small range of normal movement, provision is lmadeA to produce the effect of an increased spring scale when the stator is moved beyond a predetermined range from its neutral position. In `the vibration absorber illustrated in Figs. 3 and 4, I .secure such a spring scale by providing sloped supporting surfaces on the supporting plate 25 and the pressure blocks 28, 32 and 35 at the points where they engage the beam springs 24 and 31.

It is one Having selected a. given spring construction with a view to obtaining the best utilization of the spring material, the actual spring dimensions are so determined as to give a spring scale required for securing a given tolerable transmitting effect and to maintain the maximum stresses in the spring material below a maximum, permissible value. I

It can be shown that in the case of a spring construction employing rectangular springs of equal'dimensions, with the lower springs loaded at two points and the upper i springs loaded at one point, as shown in Figs. 3 and 4, the smallest dimension for the spring width Z) is obtained when the ratio L points and the supporting points to the length L ofthe spring is 0.15. In an arrangement entirely omitting the upper springs and employing doubly-loaded lower springs only, the smallest spring width is obtained for of the (distance a between'tll'e loading Thel clearance under the springs or the stops. limiting the range yof deflections of the stator are so determined that the support becomes solid when Vthe stress in the deiiected springs reaches 4a predetermined of Atempered steel which rests on the pedestal 93 ofthe foundation. The stator member is compressedf downwardly by means of a second set of beam springs 94 similar` lto the beam springs 91 through 'the actio'n 'of'a yoke 95 and bolts 96. f

In Fig. 6 is shown another modificationof myv invention wherein the spring members are clamped to both the vstator member and the foundatiomand spring actions of the same character are secured for both downward and upward deflections, of the springs, permitting the full utilization of the spring material without an undue increase of the spring stiffness resulting from the employment of additional spring members for restricting thev motion of the'stator of a range wherein the lower spring aggregate is always compressed in the same direction. Two sets of-spring members 101 and 102 have their ends secured to a pedestal 103 by means of bolts 104. The two spring members are spaced from each other by means of spreader blocks 105. The statorf member 106 has a lateral projection 107 which extends into the space between the spring members. is clamped to the same at two points 108 and 109 that are spaced from each other and from the ends of the spring members. By proper choice of the relative spacings between the points at which the spring members are clamped to the pedestal 103 and to the stator projection 107, respectively, any required degree of spring stiffness and loading efiiciencymay be .secured. i

In Fig. 7 is shown a modification of the arrangement shown in Fig. 6. Sets of double cantileversprings 111 are clamped in spaced relation to a standard or foundation 112 by means of bolts 113. The springs are spaced-from each otherV by spreader blocks 114. A horizontal stator extension 115 is provided with spring nests 116 supporting hardenedplates 117 co-operating with the free ends of the springs 111.

The hardened plates 117 are secured to A the stator extensions 115 by means of bolts have a sloped surface to give 119 and may the springs a climbing scale.

In the construction shown in Fig. 7, the springs are initially bent upwardly and are brought into the horizontal position under the action of the stator weight. Such construction is not absolutely necessary, however, as the springs may-be initially straight and bent downwardly in the neutral position when carrying the full stator weight. The latter construction is slightly cheaper since it saves the forming of the springs and permits the employment of straight spring beams. v.

In the constructions shown in Figs. 6 and 7, the load is carried on all of the springs' .x and accordingly the stress is` better distrib? uted on the springs with a consequentlyl better utilization of the resiliency of the same for the elimination of the undesirable effects of periodically acting forces. Y

In Fig. 8 is shown a modification of my invention which is of advantage in large machines wherein it is desirable to provide additionalsafety against displacement -of the stator fromits central position. The

-stator`121 is supported on coil springs 122 by means of lateral projections 123 extending in a horizontal plane through the axis of rotation. To prevent the stator from displacement -in lateral and vertical directions without interfering with the slight rotational movement which is necessary for securing the action of the vibration absorbing springs 122, flexible straps 124 of. resilient material such as steel are secured in a radial direction in the horizontal and vertical planes between rejections 125 of the stator and the foun ation. i f

'Security against radial, dis lacement of the stator may also be obtaine by e(properly mounting the spring-members us in the arrangements shown in Figs struction of such character, as applied to the .3to8. Acon-K presents a considerable larger resistance to p deflections in lthe lateral direction than in the vertical direction. Y v

Certain features of my invention are described` in an article which appeared in the Electrical Journal for May, 1924.

My invention is not restricted to the particular arrangements van-d details of constructlon shown and described hereinbefore but may be utilized in a variety of other ways and I desire that the language of the appended claims shall be construed broadly to cover all modifications falling within the scope of my invention.

I claim as my invention 1. A member exposed to periodically varying forces tending to move the same, a second member co-operating with said first mentioned member to oppose said movement, and a resilient connection between said members comprising two flexed spring aggregates support-ed by one of said members and holding the other of said members therebetween, one-of said spring aggregates' comprlslng a beam spring held at its ends and l flexed at one. point intermediate said endsL and the other of said spring aggregates 'comprlsmg a beam springl held at its ends and flexed at two points spaced from each other and from said ends.

2. A machine comprising a rotor and al stator concentric with saidrotor, a foundation for said machine, said stator being exposed to periodically varying forces-tending to rotate the same around its axis, a pair of torque transmitting connections between said said lower spring member and havin a relatively small spring scale as compare to that of the lower spring member.

3. A member exposed to periodically varying forces tending to move the same, a

second member co-operating with said first mentioned member to oppose said movement and a resilient connection between said members comprising a plurality of beamsprin'gs of substantially identical dimensions are ranged in' two aggregates supported by one of. said members and holding the yother of said members therebetween, one of ysaid spring aggregates comprising 'a beamspringr held at its ends and flexed at one point intermediate said ends and the other of said spring aggregates comprising a beam spring v'held at its ends and flexed at two points spaced from each other andfrom said ends.

4. The combinationA lwith a dynamo-electric machine having a stator and a rotor, said stator being exposedvto pulsating torsional forces, of'a foundation, rotor-supporting bearings rigidly supported in a horizontal'position upon said foundation, means for restraining said stator againstl any motion other than circular said means comprising` a ,l

' spring mounting Vconstituting the sole supportl of said stator upon said foundation,

l said Amounting comprising legs extending from substantially diametrically" opposite sides of the stator in a `horizontal central .l plane therethrough, a pedestal member rigsional forces, of a foundation, rotor-supporting bearings rigidly supported lin a horizontal position upon said foundation, and a spring mounting constituting the sole -sup- L port of said stator upon said `foundation,

said mounting comprising legs extending from substantially diametrically opposite sides ofthe stator in av horizontal central plane"4 therethrough, a pedestal member rigidly extending from said foundation on each side of the stator ,to support the corresponding leg, each pedestal having a supporti-ng member disposed below the legs, a lower beam spring carried 'by said supporting member and underlying the leg to support said stator,anupper beam` sprlng disposed on the top of the leg, a yoke-for downwardly pressingsaid upper beam spring and means for fixing the distance" of said yoke from said supporting member to determine the p to the foundation.'

A site sides of the stator and having flat sides y disposed substantially radially whereby they normal position of the stator with .respect 6. A dynamb-electric machine comprising a' stator and a rotor having a pulsatory torque, and `beam spring supports on oppoare adapted to yield only -in substantially tangential directions; with respect to lthe rotor at the points of application of the spring supports.

7.-'I`he combination with aydyna'm'o-electric machine having a, stator and a rotor, said stator being exposed to pulsating tor- I i .l v L sional forces, of a foundation, rotor-supporting bearings rigidly supported upon said foundation, and a spring mounting constituting the sole support of v said stator upon said foundation and comprising stator legs v and beam springs" secured to said legs and said foundation at spaced points, respectively, said springs being disposed parallel to the stator axis andhaving a rectangular cross section of which twosides are disposed in a substantially radial-direction with respect to the center of the machine and are longer than the other sides.

8. A variable-torque` dynamo-electric machine and support having in' combination, a

dynamo-electric machinefa frame, a plurality of beam springs rigidly secured to the frame and the machine and arranged on Vopposite sides of the machine lsubstantially radially Withrespect to the motor axis, the springs being stiEv in radial and longitudinal directions to support the machine and to prevent jsubstantial bodily movement thereof, and springy in the directionanormaltov the radial to permit rotational vibrations of the machine due to variations of machine torque without transmission thereof to the frame.

9. A variable torque dynamo electric machineA and supporthaving in combination, a dynamo electricv machine, a frame, a plurality of fiat arms rigidly secured to the ,frame and the machine and arranged at each side of the machine substantially radially with respect to the machine axis,4theL varms being stiff fin vradial and longitudinal directions to support the machine and to prevent v'substagntial bodily movement thereof, and

springy inthe direction normal to the radial to vpermit rotational vibrations of the ma- 'chine due to variations of machine torque without transmission thereof to the frame.'

In testimony whereof,l I have hereunto subscribed my name this 23rd day of vrSepamber, 1932.

CARL a. soDERBE'RGi 

